Factorial Design Part II

Interaction Variability TOTAL VARIABILITY SStotal Between Treatment Variability SSbetween treatment Within Treatment Variability SSWithin/ERROR Factor A Variability SSA Factor B Variability SSB Interaction Variability SSAB

SS df MS F SS df MS F Source Between [(T2/n)] - G2/N Within/Error   SS df MS F Between [(T2/n)] - G2/N ab-1 SSBT/dfbt MSBT/MSE Within/Error [(x2) – (T2/n)] or…SST-SSBT N-ab SSE/dfE Total (x2) - G2/N N-1 Source   SS df MS F Factor A (Ta2/n) - G2/N a-1 SSA/dfa MSA/MSE Factor B (Tb2/n) - G2/N b-1 SSB/dfb MSB/MSE Interact SSBT-SSA-SSB dfbt– dfA-dfB SSAB/dfab MSAxB/MSE

Using RC ….so much easier

Last Class Full Example Does playing soccer lead to neurological damage from heading the ball? Perhaps…but maybe the results don’t show up until later. Downs et al (2002) collect data on older and younger soccer players and swimmers. They administer a cognitive test to these subjects and measure the results. Do the data suggest that cognitive ability differs depending on the sport played and age of participant? Alpha = .05   Soccer Swimming Younger 2, 4, 5, 3, 6 7, 7, 5, 5, 6 Older 3, 1, 2, 3, 1 10, 8, 7, 7, 8

Hand Calc Results Source SS df MS F p Model Error Total 100 24 124 3   SS df MS F p Model Error Total 100 24 124 3 16 19 33.33 1.5 6.53 22.22 < .05 Source   SS df MS F p Sport Age SxA 80 20 1 53.3 13.33 < .05 > .05

Factorial ANOVA steps Define null and alternative for: Set alpha Omnibus, main effects, and interaction Set alpha Calculate sums of squares: Total, Between treatments, Error/within Partition SS between treatments into: SS for each main effect and SS interaction Calculate mean squares and F ratios: omnibus, main effects, interaction Identify F critical values for: Make decisions about rejecting the null Interpret results

Social support in Stressful Situations The subjects in an experiment were told that they were going to experience a mildly painful medical procedure. They were asked to rate how much they would like to wait with another subject, who was a confederate, and either identified as male or female. The two independent variables were the gender of the subject, and the gender of the confederate. 20 subjects participated; 5 in each group. The data are presented in the table below. Conduct a 2-way ANOVA to examine the effect of these two variables on the subjects' desire to wait with another person ( = .05).   Confederate Subject Male Female M = 4 x = 20 x2 = 88 x2 = 86 M = 5 x = 25 x2 = 129 M = 8 x = 40 x2 = 324

Social Support ANOVA table Source   SS df MS F Model Error Total Source   SS df MS F Subject Confed SxC   Confederate Male Female Subject 4 5 8 6.5 4.5 6

Participant Gender and Confederate Gender Predicting Preference to Wait with Another Person

Reporting the results of a 2-Way ANOVA The 2x2 ANOVA indicated that there was an overall effect, F (3, 16) = 13.03, p < .05, suggesting the independent variables influenced how much people wanted to wait with someone else. There was a significant main effect of subject gender, F (1, 16) = 22.73, p < .05; women indicated a greater desire to wait with someone else than men. The main effect of confederate gender was also significant, F (1, 16) = 8.18, p < .05. People preferred to wait with a woman rather than a man. Finally, the interaction effect was significant, F (1, 16) = 8.18, p < .05. Males’ ratings were the same regardless of whether the confederate was male (M = 4) or female (M=4) but females’ ratings were higher if the confederate was a female (M 8), rather than a male (M = 5).

Reporting the results of a 2-Way ANOVA The 2x2 ANOVA indicated that there was an overall effect, F (3, 16) = 13.03, p < .05, suggesting the independent variables influenced how much people wanted to wait with someone else. There was a significant main effect of subject gender, F (1, 16) = 22.73, p < .05; women indicated a greater desire to wait with someone else than men. The main effect of confederate gender was also significant, F (1, 16) = 8.18, p < .05. People preferred to wait with a woman rather than a man. Finally, the interaction effect was significant, F (1, 16) = 8.18, p < .05. Males’ ratings were the same regardless of whether the confederate was male (M = 4) or female (M=4) but females’ ratings were higher if the confederate was a female (M 8), rather than a male (M = 5).

Reporting the results of a 2-Way ANOVA The 2x2 ANOVA indicated that there was an overall effect, F (3, 16) = 13.03, p < .05, suggesting the independent variables influenced how much people wanted to wait with someone else. There was a significant main effect of subject gender, F (1, 16) = 22.73, p < .05; women indicated a greater desire to wait with someone else than men. The main effect of confederate gender was also significant, F (1, 16) = 8.18, p < .05. People preferred to wait with a woman rather than a man. Finally, the interaction effect was significant, F (1, 16) = 8.18, p < .05. Males’ ratings were the same regardless of whether the confederate was male (M = 4) or female (M=4) but females’ ratings were higher if the confederate was a female (M 8), rather than a male (M = 5).

Calculating simple main effects When there is a significant interaction, we will perform a separate analysis of variance for each column (or row) to examine individual group differences. Caffeine, Studying, and Exam Performance No Coffee 1-2 Cups > 2 Cups   Studied 82 95 80 Did not Study 74 73 60

Calculating simple main effects One-way ANOVA for No Coffee condition: compare studied vs. not Caffeine, Studying, and Exam Performance No Coffee 2 Cups > 2 Cups   Studied 82 95 80 Did not Study 74 73 60 One-way ANOVA

Calculating simple main effects One-way ANOVA for 2 cups condition: compare studied vs. not Caffeine, Studying, and Exam Performance 1-2 Cups > 2 Cups   Studied 95 80 Did not Study 73 60 One-way ANOVA

Calculating simple main effects One-way ANOVA for > 2 cups condition: compare studied vs. not Caffeine, Studying, and Exam Performance > 2 Cups   Studied 80 Did not Study 60 One-way ANOVA

Calculating simple main effects And/or… 4. One-way ANOVA for the studied condition: no vs. 2 vs. >2 cups 5. One-way ANOVA for the did not study condition: Caffeine, Studying, and Exam Performance No Coffee 1-2 Cups > 2 Cups   Studied 82 95 80 Did not Study 74 73 60 One-Way ANOVA One-Way ANOVA

More practice with Interpretation

Caspi et al.. DV: self-reported depression symptoms IV #1: number of stressful life events participants experienced in past year (5 levels) IV #2: Genetic risk (3 levels: s/s allele; s/l allele, or l/l allele)

Kong et al. (2008) DV: number of words remembered (# Yes responses) IV #1: Diagnosis (2 levels: Dissociative Identity Disorder-DID and Controls IV#2: Condition (3 levels: List A, List B, Distractor List)

DV: Physical aggression (higher suggests more aggression) McQuade (2017) DV: Physical aggression (higher suggests more aggression) IV#1: Children’s level of physical victimization (i.e., how much bullied; 2 levels low and high) IV#2: Children’s executive functioning skills (EF: cognitive abilities; 3 levels: low, average, high)  

IV#1: Harsh parenting (2 levels: - 1 SD = low and + 1 SD = high) Erath et al. (2009) DV: externalizing problems (e.g., aggression, noncompliance, rule-breaking) IV#1: Harsh parenting (2 levels: - 1 SD = low and + 1 SD = high) IV#2: Girls’ stress reaction (e.g., how they respond physiologically to a stressful task; 2 levels: Higher SCLR = high stress reaction; Lower SCLR = low stress reaction)